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$\sum_{r=1}^n=(f(1)-f(2))+(f(2)-f(3))+(f(3)-f(4))+\dots (f(n-1)-f(n))+(f(n)-f(n+1))=$
$\sum_{r=1}^n=f(1)+(-f(2)+f(2))+(-f(3)+f(3))+(-f(4)+f(4))+\dots (-f(n))+f(n))-f(n+1)=$
$f(1)-f(n+1)$
similar for the other formulas.
can anyone please explain how does the formula work? i cant understand. if i sub r=1 into the first eq, i would get f(1)-f(1+1) , not f(1)-f(n+1), when should i use the first and when should i use the second formula, can you givr relevant examples please? much appreciated!
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